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Functional Analysis

Title:
An Algebraic Spin and Statistics Theorem

Abstract: A spin-statistics theorem and a PCT theorem are obtained in the context of
the superselection sectors in Quantum Field Theory on a 4-dimensional
space-time. Our main assumption is the requirement that the modular groups of
the von Neumann algebras of local observables associated with wedge regions act
geometrically as pure Lorentz transformations. Such a property, satisfied by
the local algebras generated by Wightman fields because of the
Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.

Comments:

15 pages, plain TeX, an error in the statement of a theorem has been corrected, to appear in Commun. Math. Phys